The state's current governor, Republican Asa Hutchinson, has been in the job since 2015 and can not be elected again due to the state's two-term rules. She is the author of the New York Times bestseller "Speaking for Myself", a former Fox News contributor, and serves on the Fulbright board.
Acosta, who previously served as CNN's Chief White House correspondent, got into numerous squabbles with Sanders and other Trump officials duing briefings.
When Sanders succeeded Sean Spicer as White House press secretary in 2017, she was only the third woman to serve in the position and did so for almost two years - with her tenure marked by a combative relationship with the press. Republican state Sen. Jim Hendren, who is also a nephew of Hutchinson's, is considering a run.
Her video featured photographs of Mr Trump and criticisms of socialism, "cancel culture", and the Green New Deal.
Ms Sanders said: "We've seen violence in our streets, at a Congressional baseball practice, and our Capitol".
Acosta briefly had his press badge suspended by the White House after he had an altercation with an intern trying to take back the microphone during a testy back-and-forth with then-President Trump in 2018. In her home state of Arkansas, though, she is quite popular.
"With the radical left now in charge of Washington, your governor is your last line of defense". "The radical left's solution is to impose government control and censorship from the top down". I will not bow down to the radical left. No Democrats have announced a run for the seat. Shortly after her departure, Sanders admitted she was "very seriously looking at" a run soon and felt like she was "called" to enter the race.
"My opponents will do everything in their power to destroy me", Sanders said. "And never let them silence you".
Trump in November won the state by almost 28 percentage points, one of the biggest margins in his ultimate loss to Biden. Sanders' almost 8-minute video prominently features photos of Trump, along with references to his favourite targets such as "cancel culture", socialism and the Green New Deal.